Kalman filter, particle filter, IMM, PDA, ITS, random sets... The number of useful object-tracking methods is exploding. But how are they related? How do they help track everything from aircraft, ...missiles and extra-terrestrial objects to people and lymphocyte cells? How can they be adapted to novel applications? Fundamentals of Object Tracking tells you how. Starting with the generic object-tracking problem, it outlines the generic Bayesian solution. It then shows systematically how to formulate the major tracking problems – maneuvering, multiobject, clutter, out-of-sequence sensors – within this Bayesian framework and how to derive the standard tracking solutions. This structured approach makes very complex object-tracking algorithms accessible to the growing number of users working on real-world tracking problems and supports them in designing their own tracking filters under their unique application constraints. The book concludes with a chapter on issues critical to successful implementation of tracking algorithms, such as track initialization and merging.
•We address the integration of passenger demand oriented train scheduling and rolling stock circulation for urban rail transit lines.•We propose three optimization methods to construct the train ...schedule and rolling stock circulation plan simultaneously.•We investigate the benefits of the integration, the performance comparison between the proposed approaches, and the sensitivity analysis.•Our integrated model and solution methods can be used in rail practice to obtain better train schedules and circulation plans automatically.
We study the integration of train scheduling and rolling stock circulation planning under time-varying passenger demand for an urban rail transit line, where the practical train operation constraints, e.g., the capacity of trains, the number of available rolling stocks, and the entering/exiting depot operations, are considered. Three solution approaches are proposed to solve the resulting multi-objective mixed-integer nonlinear programming (MINLP) problem to deliver both an irregular train schedule (i.e., departure and arrival times of all train services) and a rolling stock circulation plan (including entering/exiting depot operations of rolling stocks and connections between train services) simultaneously. We first present an iterative nonlinear programming (INP) approach, where the solutions of the original MINLP problem are obtained by solving a nonlinear programming problem and a mixed integer linear programming (MILP) problem iteratively. Moreover, an equivalent MILP formulation of the original MINLP model is developed and an approximated MILP approach is proposed to reduce the number of constraints introduced by passenger demand. A case study is conducted based on the practical data of the Beijing Yizhuang line, where the three proposed approaches are compared with a state-of-the-art approach and a practical method used by the traffic planners. This comparison shows the effectiveness and efficiency of the three proposed approaches.
This paper considers an integrated supplier selection and inventory control problem for a multi-echelon inventory system with an order-splitting policy. A buyer firm consisting of one warehouse and N ...identical retailers procures a type of product from a group of potential suppliers; the acquisition of the warehouse takes place when the inventory level depletes to a reorder point R, and the order Q is simultaneously split among m selected suppliers. We develop an exact analytical model for the order-splitting problem in a multi-echelon system, and formulate the supplier selection problem in a Mixed Integer Nonlinear Programming (MINLP) model. This model determines the optimal inventory policy that coordinates stock levels between each echelon of the systems while properly allocating orders among selected suppliers to maximize the expected profit. For verification and validation of the proposed mathematical model, we conduct several numerical analyses and implement simulation models which helps us demonstrate the model’s solvability and effectiveness.
•We study the supplier selection and order allocation problem.•We formulate a mixed integer nonlinear programming model.•We provide illustrative examples and computational analysis.•We verified the model through simulation and conduct sensitivity analysis.
Decision trees are widely-used classification and regression models because of their interpretability and good accuracy. Classical methods such as CART are based on greedy approaches but a growing ...attention has recently been devoted to optimal decision trees. We investigate the nonlinear continuous optimization formulation proposed in Blanquero et al. (2020) for training sparse optimal randomized classification trees. Sparsity is important not only for feature selection but also to improve interpretability. We first consider alternative methods to sparsify such trees based on concave approximations of the l0 “norm”. Promising results are obtained on 24 datasets in comparison with the original l1 and l∞ regularizations. Then, we derive bounds on the VC dimension of multivariate randomized classification trees. Finally, since training is computationally challenging for large datasets, we propose a general node-based decomposition scheme and a practical version of it. Experiments on larger datasets show that the proposed decomposition method is able to significantly reduce the training times without compromising the testing accuracy.
•l0-based regularization terms induce sparsity in multivariate randomized classification trees.•new lower and upper bounds on the VC dimension of multivariate randomized classification trees.•node-based decomposition methods for multivariate randomized classification trees.
The important focus of the energy strategy of the European Union relies on the concept of zero energy building (ZEB), which is, by definition, a building that roughly produces yearly as much ...renewable energy as it consumes. This article proposes an enhanced mixed-integer nonlinear programming model for optimal sizing of photovoltaic (PV) and battery energy storage systems to comply with the definition of a ZEB. A salient novel feature of the proposed model is that it factors in the environmental impacts, computed through rigorous life cycle assessment methodology, of buying electricity from the grid and manufacturing battery and PV systems. Furthermore, an adjustable parameter is introduced to make the model adaptive from the perspective of the building owner's willingness-to-pay for environmental impacts. The proposed model is then rigorously reformulated, managing to accumulate its nonlinearity in only one constraint per time interval. Eventually, the reformulated model is linearized to a mixed-integer linear programming model using the McCormick relaxation technique. The case study conducted on archetypal buildings in Luxembourg reveals that the proposed McCormick-based linear model is able to provide high accuracy results with reasonable computational effort.
► We address the main challenges to the security constrained optimal power flow (SCOPF) computations. ► We discuss SCOPF issues such as the use of a limited number of corrective actions in the ...post-contingency states and the modelling of voltage and transient stability constraints. ► We present techniques aimed to reduce the size of the SCOPF problem and to handle discrete variables in SCOPF. ► We address the extension of the SCOPF formulation to take into account operation planning uncertainty.
This paper addresses the main challenges to the security constrained optimal power flow (SCOPF) computations. We first discuss the issues related to the SCOPF problem formulation such as the use of a limited number of corrective actions in the post-contingency states and the modeling of voltage and transient stability constraints. Then we deal with the challenges to the techniques for solving the SCOPF, focusing mainly on: approaches to reduce the size of the problem by either efficiently identifying the binding contingencies and including only these contingencies in the SCOPF or by using approximate models for the post-contingency states, and the handling of discrete variables. We finally address the current trend of extending the SCOPF formulation to take into account the increasing levels of uncertainty in the operation planning. For each such topic we provide a review of the state of the art, we identify the advances that are needed, and we indicate ways to bridge the gap between the current state of the art and these needs.
We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space ...of (multivariate and non-discrete) probability distributions centered at the uniform distribution on the training samples, and we seek decisions that perform best in view of the worst-case distribution within this Wasserstein ball. The state-of-the-art methods for solving the resulting distributionally robust optimization problems rely on global optimization techniques, which quickly become computationally excruciating. In this paper we demonstrate that, under mild assumptions, the distributionally robust optimization problems over Wasserstein balls can in fact be reformulated as finite convex programs—in many interesting cases even as tractable linear programs. Leveraging recent measure concentration results, we also show that their solutions enjoy powerful finite-sample performance guarantees. Our theoretical results are exemplified in mean-risk portfolio optimization as well as uncertainty quantification.
In this paper, a two-stage procedure is proposed in order to solve the centralized self-healing scheme for electrical distribution systems. The considered self-healing actions are the reconfiguration ...of the distribution grid and, if needed, node and zone load-shedding. Thus, the proposed procedure determines the status of the switching devices in order to effectively isolate a faulty zone and minimize the number of de-energized nodes and zones, while ensuring that the operative and electrical constraints of the system are not violated. The proposed method is comprised of two stages. The first stage solves a mixed integer linear programming (MILP) problem in order to obtain the binary decision variables for the self-healing scheme (i.e., the switching device status and energized zones). In the second stage, a nonlinear programming (NLP) problem is solved in order to adjust the steady-state operating point of the topology found in the first stage (i.e., correction of the continuous electrical variables and load-shedding optimization). Commercial optimization solvers are used in the first stage to solve the MILP problem and in the second stage to solve the NLP problem. A 44-node test system and a real Brazilian distribution system with 964-nodes were used to test and verify the proposed methodology.
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